One configuration of a conventional refrigeration appliance includes at least one wall, such as a door, to provide access to a fresh food compartment or a freezer compartment, allowing access to the stored items within the refrigeration appliance. Conventional refrigeration appliances typically include accessories, such as shelves or bins, that are mounted to the interior of the door for storing fresh and frozen food items within the compartment. For example, U.S. Pat. App. No. 2014/0360220 to Rackley et al. discloses such a conventional refrigeration appliance. Such a configuration is convenient, as door-mounted bins increase the amount of storage space that is easily accessed by the user, rather than having to reach into the interior areas of the refrigeration appliance. Door-mounted bins can also provide the convenience of configurations beneficial to store items such as bottles, cans, and/or other food or beverage containers.